Minimal stencil finite volume scheme with the discrete maximum principle

作者:Lipnikov K; Svyatskiy D; Vassilevski Yu*
来源:Russian Journal of Numerical Analysis and Mathematical Modelling, 2012, 27(4): 369-385.
DOI:10.1515/rnam-2012-0020

摘要

We propose a cell-centered finite volume (FV) scheme with the minimal stencil formed by the closest neighbouring cells. The discrete solution satisfies the discrete maximum principle and approximates the exact solution with second-order accuracy. The coefficients in the FV stencil depend on the solution; therefore, the FV scheme is nonlinear. The scheme is applied to a steady state advection-diffusion equation discretized on a general polygonal mesh.

  • 出版日期2012